Grants and Contributions:

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Title:

Modular forms and arithmetic geometry

Agreement Number:

RGPIN

Agreement Value:

$215,000.00

Agreement Date:

May 10, 2017 -

Organization:

Natural Sciences and Engineering Research Council of Canada

Location:

Ontario, CA

Reference Number:

GC-2017-Q1-03357

Agreement Type:

Grant

Report Type:

Grants and Contributions

Additional Information:

Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023)

Recipient's Legal Name:

Kudla, Stephen (University of Toronto)

Program:

Discovery Grants Program - Individual

Program Purpose:

Imagine a crystal as a lattice of atoms arranged in space according to a regular repeating pattern. Theta functions, the mathematical objects which encode the locations of the lattice points (atoms) as one moves outward from a fixed point, have many remarkable properties and have been studied since the 19th century. Recently, much more complicated theta functions have been introduced, for example in the study of lattice points inside or outside the light cone Minkowski space. Still more exotic ones occur in the study of arithmetic geometry -- the theory of whole number solutions to polynomial equations. Theta functions are special cases of a wider class of functions, modular forms and automorphic forms. The goal of this research is to develop new types of theta functions and automorphic forms and to investigate their applications in number theory and their connections to physics, in particular, to the counting functions which arise in string theory.